pdfkap {lmomco} | R Documentation

## Probability Density Function of the Kappa Distribution

### Description

This function computes the probability density of the Kappa distribution given parameters (xi, α, kappa, and h) of the distribution computed by `pargev`. The probability density function of the distribution is

f(x) &= α^{-1} [1-kappa(x - xi)/α]^{1/k-1} times [F(x)]^{1-h}

where f(x) is the probability density for quantile x, F(x) is the cumulative distribution function of the distribution (`cdfkap`)), xi is a location parameter, α is a scale parameter, and kappa is a shape parameter.

### Usage

    pdfkap(x, para)

### Arguments

`x` | A real value.
`para` | The parameters from `parkap` or similar.

### Value

Probability density (f) for x.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

Sourced from written communication with Dr. Hosking in October 2007.

### See Also

`cdfkap`, `quakap`, `parkap`

### Examples

    kap <- vec2par(c(1000,15000,0.5,-0.4),type='kap')
    F <- nonexceeds()
    x <- quakap(F,kap)
    check.pdf(pdfkap,kap,plot=TRUE)

[Package lmomco version 0.92 Index]